I need to simulate the interference of two sinewaves
If you'd like to visualize interference in 3D, that can also be done. The animation below illustrates 5 sine waves interacting with each other in 3D. The coloring is done by taking a slice through the combined waves and assigning colors to the intensity of the wave. Using shaders is fast enough that the images can be generated in real time. This solution is based on an an antenna/radar example here,



Details for visualizing 2 interfering waves on a surface  - (Tested on Blender 2.92)


To visualize 2 waves with interference, some simple geometry is setup for the visualization. The key is using the wave texture. A plane is used to visualize the waves, and 2 spheres are used to visualize and control the origin of the waves.



Shaders are used to generate the visualization of the interference. The wave node texture performs the math for each wave and a math node sums the waves together to see the interference. The full shader for 2 interfering waves is shown below. This shader is named 'wave'



The nodes in the red frame calculate the sine waves and when summed together generate the interference patterns in 3D.
The nodes in white are used to specify the origin of the waves. To help with the visualization, this is done using the two spheres in the geometry that were called Wave Source 1 and Wave Source 2. The text Coordinate node is used to get their origin and then use that to set the origin of the waves.
The nodes in the two blue frames are used to set the wavelength and phase of the waves. The wavelength in blender defaults to 1mm, so it is scaled to meters. The phasing is defined in radians so it is scaled to degrees. If the phasing is animated, the sign will control the direction of travel of the wave.
The nodes in the green frame control how the calculated wave intensity is visualized. This node scales the wave intensity to a value between 0 and 1, then uses a color ramp to make it red where positive and blue where negative. Transparency is used to set the color emissivity to zero where there the intensity is near zero.
Note this shader defines the intensity everywhere. When it is applied to an object, it will show the wave intensity there.


In this example, the shader called 'wave' is applied to a plane called 'surface'. This will show the wave intensity on that plane.



Additional slices can be visualized by adding more planes to the scenes.



The blender 2.92 model for this example is available here - 

Extension #1 - Visualizing as a 3D wave


Add a volume for visualizing the waves.



Copy and modify the previous surface shader. The turquoise frame shows the changes for volume rendering.



The math block on the left scales the input to 0..1 so it will work with a color ramp. The color is applied to a 'Principled Volume' color input. This sets to color of the location in the volume.
The math node connected to the alpha is used to scale the density which sets the opacity of the volume.


Adjust light and setting to get desired look.

The blender 2.92 model for this example is available here - 
References - See creating mesh on an isosurface

Extension #2 - Visualizing the interference as a surface wave


Turn on experimental features for rendering.


Add a subdivision multiplier to the visualization plane. Use simple subdivision. Set adaptive.




Add a displacement node to the shader.


The blender model for this example is available here - 
References

2.8 Adaptive Subdivision


Extension #3 - Multiple wave sources
By adding more wave sources, these kinds very complex wave interactions can be visualized.


This Blend file contains the model used to generate the animation - 
This blend file was generated in Blender 2.90

References
References - See http://exnumerus.blogspot.com/2021/02/visualizing-3d-sine-wave-using-blender.html This shows an application in Blender to illustrate how phased array radars and antennas work.